Rate gyroscopes are sensors that measure rotation rate. Rate gyroscopes have uses in many commercial and military applications including, but not limited to, inertial navigation, vehicular skid control, and platform stabilization.
A vibratory rate gyroscope is a sensor that responds to a rotation rate by generating and measuring Coriolis acceleration. Coriolis acceleration is generated by any object (such as a proof-mass) that has some velocity relative to a rotating reference frame. In vibratory rate gyroscopes, one or more proof-masses are suspended from flexures and made to oscillate thus providing a velocity necessary to generate Coriolis acceleration. Measurement of the resulting Coriolis acceleration can then yield an estimate of the rotation rate of the sensor.
An idealized version of such a sensor is shown in FIG. 1. In this figure a three-dimensional, mutually orthogonal coordinate system is shown for reference. The axes are arbitrarily labeled "X", "Y" and "Z", to enable description of background material as well as the invention. The axis of oscillation, which is largely coincident with the X-axis, is often referred to as the drive-mode. Coriolis acceleration is generated perpendicular to the drive-mode along the sense-mode, which lies largely along the Y-axis. The Coriolis acceleration generated by the system shown in FIG. 1 is given by: EQU a.sub.Coriolis =2.OMEGA..sub.z D.sub.x.omega..sub.x cos(.omega..sub.x t) Equation 1
where a.sub.Coriolis is the Coriolis acceleration generated along the sense-mode, .OMEGA..sub.z is the rotation rate to be measured about the Z-axis, and .omega..sub.x and D.sub.x are the frequency and magnitude of drive-mode oscillation respectively. The Coriolis acceleration causes an oscillatory displacement of the sensor along the sense-mode with magnitude proportional to the generated Coriolis acceleration. Ideally, the drive-mode is coincident with the forcing means used to sustain oscillation (located along the X-axis or drive-axis), and the sense-mode is coincident with the sensing means used to detect displacements due to Coriolis acceleration (located along the Y-axis or sense-axis). The design and fabrication of the proof-mass and the suspension will dictate the actual orientation of the drive- and sense-modes with respect to the driving and sensing axes, however. An important fact to note is that the Coriolis acceleration signal along the sense-axis is in phase with velocity of the drive-mode, which is 90 degrees out-of-phase with proof-mass displacement along the drive-mode. While the Coriolis acceleration is 90 degrees out-of-phase with the proof-mass displacement along the drive-mode, displacements along the sense-mode due to Coriolis acceleration may have a different phase relationship to the proof-mass displacement along the drive-mode depending on several factors including: the relative values of drive-mode oscillation frequency to sense-mode resonant frequency, and the quality factor of the sense-mode.
To accurately measure rotation rate, the Coriolis acceleration must be easily distinguished from other sources of acceleration. Coriolis acceleration is unique for three reasons: 1) it occurs along the sense-mode which lies largely along the Y-axis, 2) it occurs at the driven-mode oscillation frequency, .omega..sub.x, and 3) it is in phase with the velocity of the drive-mode oscillation. Further discrimination of Coriolis acceleration can be achieved using dual-mass gyroscopes that generate a differential Coriolis acceleration in response to a rate input. Note that Coriolis acceleration can be difficult to measure in the presence of quadrature error. Quadrature error results in an oscillatory acceleration having three properties (two of which are shared with Coriolis acceleration): 1) it occurs along the Y-axis, 2) it occurs at the driven-mode oscillation frequency, .omega..sub.x, and 3) it is either in phase or 180-degrees out of phase with the position (not velocity) of the drive-mode oscillation, depending on the sign of the error. For a comprehensive discussion of quadrature error, please see Clark, W. A., Micromachined Vibratory Rate Gyroscopes, Doctoral Dissertation, University of California, 1997. Thus, Coriolis acceleration and quadrature error are distinguished only by their phase relative to the driven-mode oscillation.
Forces may be applied to the gyroscope using variable air-gap capacitors formed between one or more plates (or conductive nodes) attached to the proof-mass and one or more plates (or conductive nodes) attached to the substrate. Note that electrostatic forces result between charged capacitor plates. The magnitude and direction of the force is given by the gradient of the potential energy function for the capacitor as shown below. ##EQU1##
As an example, an appropriate oscillation in the gyroscope may be generated using a force along a single axis (e.g. the X-axis). Equation 2 implies that any capacitor that varies with displacement along the X-axis will generate an appropriate force. An implementation of a pair of such capacitors is shown in FIG. 2. This capacitor configuration has a number of advantages including ample room for large displacements along the X-axis without collisions between comb fingers. By applying differential voltages with a common mode bias V.sub.DC across electrically conductive comb fingers 72, 73a and 72, 73b a force that is independent of X-axis displacement and linear with control voltage, v.sub.x is created: ##EQU2##
where C.sub.0 and X.sub.0 are the capacitance and X-axis air-gap at zero displacement respectively. An equivalent method of applying forces chooses V.sub.1, V.sub.2 such that: EQU V.sub.1 =V.sub.DC -v.sub.x V.sub.2 =-V.sub.DC -v.sub.x Equation 4
Note that in both of these cases the magnitude of the force is proportional to the control voltage, v.sub.x, and the DC bias voltage, V.sub.DC. This permits the magnitude and direction of the force to be directly controlled by varying either v.sub.x or V.sub.DC while maintaining the other voltage constant.
Many methods are known that sense motion or displacement using air-gap capacitors. Details of capacitive measurement techniques are well known by those skilled in the art. These methods may be used for detection of displacement due to Coriolis acceleration, measuring quadrature error, or as part of an oscillation-sustaining loop. Often a changing voltage is applied to two nominally equal-sized capacitors, formed by a plurality of conductive fingers, with values that change in opposite directions in response to a displacement. One method applies voltages to these sensing capacitors in a manner that generates a charge that is measured by a sense interface. (See for example: Boser, B. E., Owe, R. T., "Surface Micromachined Accelerometers," IEEE Journal of Solid-State Circuits, vol.31, pp. 366-75, March 1996., or Lemkin, M., Boser B. E., "A Micromachined Fully Differential Lateral Accelerometer," CICC Dig. Tech. Papers, May 1996, pp. 315-318.) Another method uses a constant DC bias voltage applied across two sensing capacitors. Any change in the capacitance values results in current flow that is detected by a sense interface. (See for example Nguyen, C. T.-C., Howe, R. T., "An Integrated CMOS Micromechanical Resonator High-Q Oscillator," IEEE JSSC, pp. 440-455, April 1999.) Furthermore, some methods of capacitive detection use time-multiplexing (see for example: M. Lemkin, B. E. Boser, "A Three-axis Micromachined Accelerometer With a CMOS Position-Sense Interface and Digital Offset-trim Electronics," IEEE Journal of Solid-State Circuits, pp. 456-68, April 1999) or frequency multiplexing (see for example Sherman, S. J, et. al., "A Low Cost Monolithic Accelerometer; Product/technology Update," International Electron Devices Meeting, San Francisco, Calif., December 1992, pp. 501-4) to enable electrostatic forces to be applied to a microstructure and displacement or motion of the microstructure to be sensed using a single set of capacitors. An example of an application in which time- or frequency-multiplexing of capacitor function in such a manner may prove useful includes a force-feedback loop.
Provided with a controllable force applied to a structure and a measure of the structure's deflection, the structure may be driven into oscillation using feedback. The desired oscillation is achieved by measuring the structure's displacement or velocity then determining the magnitude, and/or phase of the force or forces to apply to the structure. The measurement of the structure's displacement and the force(s) applied may be electrostatic as described above. In a dual-mass gyroscope the position or velocity detected by the sense interface often reflects relative motion between the two masses, and the forces applied to the two masses may contain a differential force component. Many methods are known to sustain drive-mode oscillation.
Because of imperfections introduced in the manufacturing process, the gyroscope driven-mode and sense-axis may not be perfectly orthogonal, thereby causing quadrature error. Imperfections in elements of the suspension are one possible cause of this non-orthogonality. Phase lag in detection circuitry can lead to quadrature error leakage into the sensor output. Results of this leakage may include large sensor output offsets, output-offset drift, and noise. In addition, large quadrature-error signals may cause saturation of sense-mode interfaces.